
\documentclass[tikz,border=10pt]{standalone}


\RequirePackage{luatex85}
\usepackage[utf8]{inputenc}
\usepackage{amsmath, amssymb, amsfonts, accents}
\usetikzlibrary{graphdrawing, graphs, arrows, shapes, automata, calc}
\usegdlibrary{trees, layered}
\usepackage{stix}


\newcommand{\Xund}{\rule{.4em}{.4pt}}
\newcommand{\IRE}{I\!RE}


\begin{document}

\begin{tikzpicture}[>=stealth, ->, auto, node distance=0.2in]

\tikzstyle{every node}=[draw=none, shape=rectangle, , outer sep = 0in];

% $(\epsilon|a^{0,\infty})(a|\epsilon)^{0,\infty}$

\small{

\begin{scope}[xshift=0.7in, yshift=0in]
    \node (a) {{
    $\begin{aligned}
        & mark ((\epsilon|a^{0,\infty})(a|\epsilon)^{0,3} )) = \big[ \\
        %
        & \quad mark ( (\epsilon|a^{0,\infty}) ) = \\
        & \quad mark ( (\epsilon|a^{0,\infty})^{1,1} ) = \big[ \\
        & \quad\quad mark ( \epsilon|a^{0,\infty} ) = \big[ \\
        & \quad\quad\quad mark ( \epsilon ) = (0,0,\epsilon), \\
        & \quad\quad\quad mark ( a^{0,\infty} ) = \big[ \\
        & \quad\quad\quad\quad mark ( a ) = (0,0,a) \\
        & \quad\quad\quad \big] = (0,0,(0,0,a)^{0,\infty}) \\
        & \quad\quad \big] = (0,0,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty})) \\
        & \quad \big] = (1,0,(1,1,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty}))^{1,1}) \\
        %
        & \quad mark ( (a|\epsilon)^{0,3} ) = \big[ \\
        & \quad\quad mark ( a|\epsilon ) = \big [ \\
        & \quad\quad\quad mark ( a ) = (0,0,a) \\
        & \quad\quad\quad mark ( \epsilon ) = (0,0,\epsilon) \\
        & \quad\quad \big] = (0,0,(0,0,a) \mid (0,0,\epsilon)) \\
        & \quad \big] = (1,0,(1,1,(0,0,a) \mid (0,0,\epsilon))^{0,3}) \\
        %
        & \big] = (1,0,
           (1,0,(1,1,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty}))^{1,1}) \\
           & \quad\quad\quad \cdot (1,0,(1,1,(0,0,a) \mid (0,0,\epsilon))^{0,3})
           )
    \end{aligned}$
    }};
\end{scope}

\begin{scope}[xshift=4in, yshift=0in]
    \node (a) {{
    $\begin{aligned}
        & enum (1,1, \; (1,0,
            (1,0,(1,1,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty}))^{1,1}) \\
            & \quad\quad\quad\quad\quad\quad \cdot (1,0,(1,1,(0,0,a) \mid (0,0,\epsilon))^{0,3})
            ) \;) = \big[ \\
        %
        & \quad enum (2,1, \; (1,0,(1,1,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty}))^{1,1}) \;) = \big[ \\
        & \quad\quad enum (3,1, \; (1,1,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty})) \;) = \big[ \\
        & \quad\quad\quad enum (4,2, \; (0,0,\epsilon)) = (4,2, \; (0,0,\epsilon) \;) \\
        & \quad\quad\quad enum (4,2, \; (0,0,(0,0,a)^{0,\infty}) \;) = \big[ \\
        & \quad\quad\quad\quad enum (4,2, \; (0,0,a)) = (4,2, \; (0,0,a) \;) \\
        & \quad\quad\quad \big] = (4,2, \; (0,0,(0,0,a)^{0,\infty}) \;) \\
        & \quad\quad \big] = (4,2, \; (3,1,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty})) \;) \\
        & \quad \big] = (4,2, \; (2,0,(3,1,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty}))^{1,1}) \;) \\
        %
        & \quad enum (4,2, \; (1,0,(1,1,(0,0,a) \mid (0,0,\epsilon))^{0,3}) \;) = \big[ \\
        & \quad\quad enum (5,2, \; (1,1,(0,0,a) \mid (0,0,\epsilon)) \;) = \big[ \\
        & \quad\quad\quad enum (6,3, \; (0,0,a) ) = (6, 3, \; (0,0,a) \;) \\
        & \quad\quad\quad enum (6,3, \; (0,0,\epsilon) ) = (6, 3, \; (0,0,\epsilon) \;) \\
        & \quad\quad \big] = (6,3, \; (5,2,(0,0,a) \mid (0,0,\epsilon)) \;) \\
        & \quad \big] = (6,3, \; (4,0,(5,2,(0,0,a) \mid (0,0,\epsilon))^{0,3}) \;) \\
        %
        & \big] = (6,3, \; (1,0,
            (2,0,(3,1,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty}))^{1,1}) \\
            & \quad\quad\quad\quad\quad \cdot (4,0,(5,2,(0,0,a) \mid (0,0,\epsilon))^{0,3})
            ) \;) \\
        \end{aligned}$
    }};
\end{scope}

%\begin{scope}[xshift=2.5in, yshift=-2.4in]
%    \node (c) {{
%    $\begin{aligned}
%        & \IRE ((\epsilon|a^{0,\infty})(a|\epsilon)^{0,3} ))
%            = (1,0, (2,0,(3,1,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty}))^{1,1})
%            \cdot (4,0,(5,2,(0,0,a) \mid (0,0,\epsilon))^{0,3}))
%    \end{aligned}$
%    }};
%\end{scope}

\begin{scope}[xshift=2.4in, yshift=-1.95in]
    \graph [tree layout, grow=down, fresh nodes, level distance=0.35in] {
        "${(1, 0, \cdot)}_{\Lambda}$" -- {
            "${(2, 0, \{1,1\})}_{1}$" -- {
                "${(3, 1, |)}_{1.1}$" -- {
                    "${(0, 0, \epsilon)}_{1.1.1}$",
                    "${(0, 0, \{0,\infty\})}_{1.1.2}$" -- {
                        "${(0, 0, a)}_{1.1.2.1}$"
                    }
                }
            },
            "${4, 0, \{0,3\})}_{2}$" -- {
                "${(5, 2, |)}_{2.1}$" -- {
                    "${(0, 0, a)}_{2.1.1}$",
                    "${(0, 0, \epsilon)}_{2.1.2}$"
                }
            }
        }
    };
\end{scope}

\newcommand\xsp[1]{\hphantom{\hspace{#1em}\hspace{-0.2em}}}

\begin{scope}[xshift=-0.3in, yshift=-3.6in, sibling distance=0.6in, level distance=0.35in]
    \node[xshift=-0.2in, draw=none] {$s:$};
    \graph [tree layout, grow=down, fresh nodes] {
        a1/"${T}^{1}_{\Lambda}$" -- {
            a11/"${T}^{2}_{1}$" -- {
                a111/"${T}^{3}_{1.1}$" -- {
                    a1111/"${\varnothing}^{0}_{1.1.1}$",
                    a1112/"${T}^{0}_{1.1.2}$" -- {
                        a11121/"${a}^{0}_{1.1.2.1}$"
                    }
                }
            },
            a12/"${T}^{4}_{2}$" -- {
                a121/"${\varnothing}^{5}_{2.1}$"
            }
        }
    };
    \node at (a1)     {\xsp{2.5}\footnotesize{$\#1$}};
    \node at (a11)    {\xsp{2.5}\footnotesize{$\#1$}};
    \node at (a111)   {\xsp{2.5}\footnotesize{$\#1$}};
    \node at (a1111)  {\xsp{3.5}\footnotesize{$\#\infty$}};
    \node at (a1112)  {\xsp{3.5}\footnotesize{$\#\infty$}};
    \node at (a11121) {\xsp{4.0}\footnotesize{$\#\infty$}};
    \node at (a12)    {\xsp{2.5}\footnotesize{$\#0$}};
    \node at (a121)   {\xsp{3.0}\footnotesize{$\#\!-\!\!1$}};

    \node[yshift=-1.65in, draw=none]
    {${T}^{1} \big(
        {T}^{2} \big(
            {T}^{3} (
                {\varnothing}^{0},
                {T}^{0}({a}^{0})
            )
        \big),
        {T}^{4}(
            {\varnothing}^{5}
        )
    \big)$};
\end{scope}

\begin{scope}[xshift=1.6in, yshift=-3.6in, sibling distance=0.6in, level distance=0.35in]
    \node[xshift=-0.2in, draw=none] {$t:$};
    \graph [tree layout, grow=down, fresh nodes] {
        a1/"${T}^{1}_{\Lambda}$" -- {
            a11/"${T}^{2}_{1}$" -- {
                a111/"${T}^{3}_{1.1}$" -- {
                    a1111/"${\varnothing}^{0}_{1.1.1}$",
                    a1112/"${T}^{0}_{1.1.2}$" -- {
                        a11121/"${\varnothing}^{0}_{1.1.2.1}$"
                    }
                }
            },
            a12/"${T}^{4}_{2}$" -- {
                a121/"${T}^{5}_{2.1}$" -- {
                    a1211/"${a}^{0}_{2.1.1}$",
                    a1212/"${\varnothing}^{0}_{2.1.2}$"
                }
            }
        }
    };
    \node at (a1)     {\xsp{2.5}\footnotesize{$\#1$}};
    \node at (a11)    {\xsp{2.5}\footnotesize{$\#0$}};
    \node at (a111)   {\xsp{2.5}\footnotesize{$\#0$}};
    \node at (a1111)  {\xsp{3.5}\footnotesize{$\#\infty$}};
    \node at (a1112)  {\xsp{3.5}\footnotesize{$\#\infty$}};
    \node at (a11121) {\xsp{4.0}\footnotesize{$\#\infty$}};
    \node at (a12)    {\xsp{2.5}\footnotesize{$\#1$}};
    \node at (a121)   {\xsp{3.0}\footnotesize{$\#1$}};
    \node at (a1211)  {\xsp{3.5}\footnotesize{$\#\infty$}};
    \node at (a1212)  {\xsp{3.5}\footnotesize{$\#\infty$}};

    \node[xshift=0.4in, yshift=-1.65in, draw=none]
    {${T}^{1}\big(
        {T}^{2}(
            {T}^{3}(
                {\varnothing}^{0},
                {T}^{0}({\varnothing}^{0})
            ),
        ),
        {T}^{4}\big(
            {T}^{5}({a}^{0},{\varnothing}^{0})
        \big)
    \big)$};
\end{scope}

\begin{scope}[xshift=4.3in, yshift=-3.6in, sibling distance=0.6in, level distance=0.35in]
    \node[xshift=-0.2in, draw=none] {$u:$};
    \graph [tree layout, grow=down, fresh nodes] {
        a1/"${T}^{1}_{\Lambda}$" -- {
            a11/"${T}^{2}_{1}$" -- {
                a111/"${T}^{3}_{1.1}$" -- {
                    a1111/"${\epsilon}^{0}_{1.1.1}$",
                    a1112/"${\varnothing}^{0}_{1.1.2}$"
                }
            },
            a12/"${T}^{4}_{2}$" -- {
                a121/"${T}^{5}_{2.1}$" -- {
                    a1211/"${a}^{0}_{2.1.1}$",
                    a1212/"${\varnothing}^{0}_{2.1.2}$"
                },
                a122/"${T}^{5}_{2.2}$" -- {
                    a1221/"${\varnothing}^{0}_{2.2.1}$",
                    a1222/"${\epsilon}^{0}_{2.2.2}$"
                }
            }
        }
    };
    \node at (a1)     {\xsp{2.5}\footnotesize{$\#1$}};
    \node at (a11)    {\xsp{2.5}\footnotesize{$\#0$}};
    \node at (a111)   {\xsp{2.5}\footnotesize{$\#0$}};
    \node at (a1111)  {\xsp{3.5}\footnotesize{$\#\infty$}};
    \node at (a1112)  {\xsp{3.5}\footnotesize{$\#\infty$}};
    \node at (a12)    {\xsp{2.5}\footnotesize{$\#1$}};
    \node at (a121)   {\xsp{3.0}\footnotesize{$\#1$}};
    \node at (a1211)  {\xsp{3.5}\footnotesize{$\#\infty$}};
    \node at (a1212)  {\xsp{3.5}\footnotesize{$\#\infty$}};
    \node at (a122)   {\xsp{3.0}\footnotesize{$\#0$}};
    \node at (a1221)  {\xsp{3.5}\footnotesize{$\#\infty$}};
    \node at (a1222)  {\xsp{3.5}\footnotesize{$\#\infty$}};

    \node[xshift=0.3in, yshift=-1.35in, draw=none]
    {${T}^{1}\big(
        {T}^{2}(
            {T}^{3}(
                {\epsilon}^{0},
                {\varnothing}^{0}
            )
        ),
        {T}^{4}\big(
            {T}^{5}({a}^{0},{\varnothing}^{0}),
            {T}^{5}({\varnothing}^{0}, {\epsilon}^{0})
        \big)
    \big)$};
\end{scope}
}

\end{tikzpicture}

\end{document}

